Question
Find the \( y \)-intercept and \( x \)-intercept of the line. \[ -5 x+7 y=12 \]
Ask by Owen Davison. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The y-intercept is (0, 12/7) and the x-intercept is (-12/5, 0).
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Beyond the Answer
To find the y-intercept of the line given by the equation \(-5x + 7y = 12\), set \(x = 0\): \[ -5(0) + 7y = 12 \implies 7y = 12 \implies y = \frac{12}{7} \] Thus, the y-intercept is \(\left(0, \frac{12}{7}\right)\). Next, to find the x-intercept, set \(y = 0\): \[ -5x + 7(0) = 12 \implies -5x = 12 \implies x = -\frac{12}{5} \] Therefore, the x-intercept is \(\left(-\frac{12}{5}, 0\right)\). To summarize, the y-intercept is \(\left(0, \frac{12}{7}\right)\) and the x-intercept is \(\left(-\frac{12}{5}, 0\right)\).
